Modelling of supercritical flow conditions revisited; NewC Scheme

Abstract

A hydrodynamic numerical model for one-dimensional free-surface flows, named ‘NewC’, is presented. NewC is a finite difference scheme which has a major advantage over schemes used currently in engineering applications in that, while the algorithmic structure is of the subcritical-flow-type. it is capable of modelling subcritical, supercritical and transcritical flow conditions without requiring any changes to the governing equations. The scheme is shown to be unconditionally stable for a range of Courant numbers even for Froude numbers greater than or equal to one. The computational effort expended compares favourably with the finite difference schemes used currently. The NewC scheme has the additional advantage that it is relatively straightforward to incorporate into algorithms for the solution of flows in free-surface networks.